arXiv subjects

Yingjie Tan

Publications and source records attributed to Yingjie Tan.

3 recordsLinked to original sources

arXiv2026

DGNet: Discrete Green Networks for Data-Efficient Learning of Spatiotemporal PDEs

Spatiotemporal partial differential equations (PDEs) underpin a wide range of scientific and engineering applications. Neural PDE solvers offer a promising alternative to classical numerical methods. However, existing approaches typically require large numbers of training trajectories, while high-fidelity PDE data are expensive to generate. Under limited data, their performance degrades substantially, highlighting their low data efficiency. A key reason is that PDE dynamics embody strong structural inductive biases that are not explicitly encoded in neural architectures, forcing models to learn fundamental physical structure from data. A particularly salient manifestation of this inefficiency is poor generalization to unseen source terms. In this work, we revisit Green's function theory-a cornerstone of PDE theory-as a principled source of structural inductive bias for PDE learning. Based on this insight, we propose DGNet, a discrete Green network for data-efficient learning of spatiotemporal PDEs. The key idea is to transform the Green's function into a graph-based discrete formulation, and embed the superposition principle into the hybrid physics-neural architecture, which reduces the burden of learning physical priors from data, thereby improving sample efficiency. Across diverse spatiotemporal PDE scenarios, DGNet consistently achieves state-of-the-art accuracy using only tens of training trajectories. Moreover, it exhibits robust zero-shot generalization to unseen source terms, serving as a stress test that highlights its data-efficient structural design.

cs.LG↗

arXiv2025

S^2-KD: Semantic-Spectral Knowledge Distillation Spatiotemporal Forecasting

Spatiotemporal forecasting often relies on computationally intensive models to capture complex dynamics. Knowledge distillation (KD) has emerged as a key technique for creating lightweight student models, with recent advances like frequency-aware KD successfully preserving spectral properties (i.e., high-frequency details and low-frequency trends). However, these methods are fundamentally constrained by operating on pixel-level signals, leaving them blind to the rich semantic and causal context behind the visual patterns. To overcome this limitation, we introduce S^2-KD, a novel framework that unifies Semantic priors with Spectral representations for distillation. Our approach begins by training a privileged, multimodal teacher model. This teacher leverages textual narratives from a Large Multimodal Model (LMM) to reason about the underlying causes of events, while its architecture simultaneously decouples spectral components in its latent space. The core of our framework is a new distillation objective that transfers this unified semantic-spectral knowledge into a lightweight, vision-only student. Consequently, the student learns to make predictions that are not only spectrally accurate but also semantically coherent, without requiring any textual input or architectural overhead at inference. Extensive experiments on benchmarks like WeatherBench and TaxiBJ+ show that S^2-KD significantly boosts the performance of simple student models, enabling them to outperform state-of-the-art methods, particularly in long-horizon and complex non-stationary scenarios.

cs.LG↗

arXiv2025

Spectral Alignment as Predictor of Loss Explosion in Neural Network Training

Loss explosions in training deep neural networks can nullify multi-million dollar training runs. Conventional monitoring metrics like weight and gradient norms are often lagging and ambiguous predictors, as their values vary dramatically across different models and even between layers of the same model, making it difficult to establish a unified standard for detecting impending failure. We introduce Spectral Alignment (SA), a novel, theoretically-grounded metric that monitors the distributional alignment between layer inputs and the principal singular vectors of weight matrices. We show that a collapse in the sign diversity of this alignment is a powerful early predictor of representational collapse and training divergence. Empirical results on language models demonstrate that monitoring the SA distribution provides a significantly earlier and clearer warning of loss explosions than traditional scalar metrics. SA's low computational overhead makes it a practical tool for safeguarding model training.

cs.LG↗